1. Field of the Invention
The invention relates generally to the field of electromagnetic geophysical surveying. More specifically, the invention relates to inversion processing techniques for interpreting electromagnetic surveys in which artificial neural networks are used to generate forward response models of the survey equipment for such inversion processing.
2. Background Art
Electromagnetic survey systems and methods provide a variety of data about formations through which the well extends; including, for example, spatial distribution of resistivity in the Earth's subsurface. Such data are interpreted and evaluated, among other purposes, to improve prediction of oil and gas production from a given reservoir or field, to detect new oil and gas production zones, to provide a picture or model of subsurface formations and of reservoirs to facilitate the removal of hydrocarbons, and to enhance the process of well location.
Inversion processing provides an estimate of the material properties of a formation and/or spatial distribution of such properties in the Earth's subsurface by updating and improving an initial model of the subsurface containing a material property description of the subsurface. The updating is performed with successively better models until an optimal model is obtained. In inversion processing, a geophysical surveying instrument response to the initial Earth model is numerically calculated, typically from a set of response equations intended to represent the instrument response. The response actually measured by such instrument; if it matches the calculated response, determines that the initial Earth model is substantially correct. If the calculated response and the measured response do not substantially match, the initial model is changed or adjusted to improve the match between the measured response and the calculated response. The update can be performed by known linear optimization methods. See, e.g., Inverse Problem Theory, Tarantola, 1987. Non-linear optimization methods can also be used. See, e.g., Genetic Algorithms and Very Fast Simulated Reannealing, Ingber and Rosen, 1992. Numerical calculation of geophysical instrument responses, and in particular electromagnetic survey instrument responses, is relatively slow, even on relatively powerful computers.
An artificial neural network provides a powerful tool for interpolation between an input data set and an output data set through a distributed set of weights. The interpolation is attained by a relatively small number of multiplications and additions which can be several orders of magnitude faster than the numerical computation of survey instrument response using standard electromagnetic propagation theory. ANNs are described generally in U.S. Pat. No. 5,554,273, for example.
Certain artificial neural networks (“ANN”) known in the art consist of a lattice arrangement of neurons, or nodes, connected by synapses or links similar conceptually to the functions imputed to the neurons in the human brain. Complex ANN structures have been built using sophisticated interconnections of simple building blocks or nodes. Layers of nodes are created and interconnections established between adjacent layers, called a feedforward network. Other ANN architectures include connections between non-adjacent layers and to additional networks, called recurrent ANNs. Nodes can also be arranged into a map and connections between the nodes created and modified during training of the network as in Self Organizing Maps. See, for example, Self-Organization and Associative Memory, Kohonen, 1984.
In the human brain, information is processed by summation of all electrical impulses into a neuron which then causes the neuron to emit its own signal. Upon receiving the input electrical signals, the neuron modifies them, changing their amplitude and frequency, using an activation function. The input signals are then summed before the neuron outputs its own signal. In a similar fashion, signals input into an ANN are changed by multiplying the input by an activation function and by a scalar value called a weight. The weights and the activation function can vary from node to node in the ANN. Typically, the input (x) and the output (f(x)) values from a node are give by the expression:fk(x)=ΣwkjR(x)  (1)
where fk(x) is the output from the k-th node, wkj are the weights connecting the j-th node to the k-th node and R is the activation function. Typically R is a hyperbolic tangent (tan h(x)). After calculating the value of the activation function, the new input values for the node are summed and the output value is passed onto all the neurons directly connected with the stimulated node. The signal feeds through the network to the output nodes where the response is saved. Like the human brain, ANN's can be trained to recognize patterns or to provide an appropriate response to a given input. The weights of the network are modified during training until the output response to any given input is correct.
By using empirical pattern recognition, ANNs have been applied in many areas to provide sophisticated data processing solutions to complex and dynamic problems (i.e. classification, diagnosis, decision making, prediction, voice recognition, military target identification, to name a few). Similar to the human brain's problem solving process, ANNs use information gained from previous experience and apply that information to new problems and/or situations. The ANN uses a “training experience” (data set) to build a system of neural interconnects and weighted links between an input layer (independent variable), a hidden layer of neural interconnects, and an output layer (the results, i.e. dependant variables). No existing model or known algorithmic relationship between these variables is required, but could be used to train the ANN. An initial determination for the output variables in the training exercise is compared with the actual values in a training data set. Differences are back-propagated through the ANN to adjust the weighting of the various neural interconnects, until the differences are reduced to the user's error specification. Due largely to the flexibility of the learning algorithm, non-linear dependencies between the input and output layers, can be “learned” from experience. Several references disclose various methods for using ANNs to solve various drilling, production and formation evaluation problems. These references include U.S. Pat. No. 6,044,325 issued to Chakravarthy et al, U.S. Pat. No. 6,002,985 issued to Stephenson et al, U.S. Pat. No. 6,021,377 issued to Dubinsky et al, U.S. Pat. No. 5,730,234 issued to Putot, U.S. Pat. No. 6,012,015 issued to Tubel and U.S. Pat. No. 5,812,068 issued to Wisler et al.
In prior art techniques for training an ANN, a training set of examples is created, typically by using standard numerical simulation techniques. A training set can contain thousands of members generated from thousands of different models. Training consists of refining the set of weights of the nodes so that any given input model produces a correct output response. At the start of training, node weights are randomly selected. A model corresponding to a member of the training set is input to the neural network and one or more outputs are generated by the network. The one or more outputs are compared with raw data or a numerical estimate based on raw data. If the outputs do not match the data, the weights are then adjusted, either by back propagation (see, e.g., U.S. Pat. Nos. 5,134,685 and 5,107,442), or a non-linear optimization method such as simulated annealing to improve the match between the two sets of data. The members of the training set are input to the network one at a time until all the members have been input. All the output data and the simulation data are compared and when the weights have stabilized, i.e., when they do not change during continued training, or exposure to the training set, and the output matches the expected output for all the members of the training set, then the ANN is considered trained. An input data set that is not in the training set is then introduced into the ANN and the correct response is output. ANNs also have some ability to extrapolate responses when faced with a model containing values outside those with which it was trained.
Electromagnetic surveying, such as includes but is not limited to controlled source electromagnetic surveying, is a technique wherein an electric or magnetic field is imparted into the Earth's subsurface from the top of an area of the subsurface that is to be surveyed. Among other methods are magnetotellurics and borehole-to-surface electromagnetics. The electric and/or magnetic fields generated in response to the imparted field are measured, also at the top of the area being surveyed. Various techniques, including inversion processing, are used to infer the spatial distribution of resistivity in the Earth's subsurface in the survey area. Because of the complexity of the electromagnetic instrument response in evaluating the structure of the Earth's subsurface in three dimensions, electromagnetic survey interpretation has proven to be difficult and time consuming. A particular issue in interpreting electromagnetic survey data is the complexity of forward instrument response modeling in inversion processing using deterministic solutions. What is needed is an improved technique for forward response modeling to be used in inversion processing of electromagnetic survey data.